# Adaptive Estimation in the Nonparametric Random Coefficients Binary Choice Model by Needlet Thresholding

## Author Info

Listed author(s):
• Eric Gautier

()

(CREST)

• Erwann Le Pennec

(INRIA)

## Abstract

In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive. The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$. We prove lower bounds on the minimax risk for estimation of the density $f_{\beta}$ over Besov bodies where the loss is a power of the $L^p(\mathbb{S}^{d-1})$ norm for $1\le p\le \infty$. We show that a hard thresholding estimator based on a needlet expansion with data-driven thresholds achieves these lower bounds up to logarithmic factors.

(This abstract was borrowed from another version of this item.)

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File URL: http://crest.science/RePEc/wpstorage/2011-20.pdf
File Function: Crest working paper version

## Bibliographic Info

Paper provided by Center for Research in Economics and Statistics in its series Working Papers with number 2011-20.

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 Length: 46 Date of creation: Jun 2011 Handle: RePEc:crs:wpaper:2011-20 Contact details of provider: Postal: Bâtiment ENSAE, 5 rue Henry LE Chatelier, 91120 PalaiseauPhone: 01 41 17 60 81Web page: http://crest.scienceMore information through EDIRC

## References

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1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
2. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(03), pages 804-837, June.
3. Eric Gautier & Stefan Soderlein, 2011. "Estimating the Distribution of Treatment Effects," Working Papers 2011-25, Center for Research in Economics and Statistics.
4. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, 03.
5. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
6. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
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